Mishnah Parah 4:3: If it was burned without wood, or with any wood, even with straw or twigs, it is valid. If it was skinned and cut up, it is valid. If it was killed with intention to eat from its flesh or to drink from its blood, it is valid. Rabbi Eliezer says: Thoughts do not invalidate with a [red] heifer.

שְׂרָפָהּ שֶׁלֹּא בְעֵצִים, אוֹ בְכָל עֵצִים, אֲפִלּוּ בְקַשׁ אוֹ בִגְבָבָה, כְּשֵׁרָה. הִפְשִׁיטָהּ וְנִתְּחָהּ, כְּשֵׁרָה. שְׁחָטָהּ עַל מְנָת לֶאֱכֹל מִבְּשָׂרָהּ וְלִשְׁתּוֹת מִדָּמָהּ, כְּשֵׁרָה. רַבִּי אֱלִיעֶזֶר אוֹמֵר, אֵין מַחֲשָׁבָה פוֹסֶלֶת בַּפָּרָה:

Mishnah Parah 4:4: Anyone involved with the heifer from its start to its end [from when it slaughtered to the collecting of the ashes], his clothing becomes impure and he invalidates her [the heifer] with [any other] work [he engages in during the ritual]. If an invalidation occurs with her slaughter, the clothing does not become impure. If it occurs with the sprinkling, the clothing of anyone involved with it before the invalidation becomes impure, and the clothing of those involved with it after the invalidation does not become impure. We find that the stringency provides a leniency [in that a stringency which invalidates acts as a leniency with respect to whether the clothing is made impure]. There is always me'ilah with it [me'ilah is the transgression of benefitting from sanctified property, see tracate Me'ilah for details], and one may add wood [to the pyre while its being burnt], and it [the ritual] is performed during the day and by a priest. [Other] work [done by the priest at the same time] invalidates it, until it is made into ashes. And [other] work [done at the same time] invalidates the water [which the ashes are mixed into] until the ashes are poured in.

כָּל הָעֲסוּקִין בַּפָּרָה מִתְּחִלָּה וְעַד סוֹף, מְטַמְּאִין בְּגָדִים, וּפוֹסְלִים אוֹתָהּ בִּמְלָאכָה. אֵרַע בָּהּ פְּסוּל בִּשְׁחִיטָתָהּ, אֵינָהּ מְטַמְּאָה בְגָדִים. אֵרַע בָּהּ בְּהַזָּיָתָהּ, כֹּל הָעוֹסֵק בָּהּ לִפְנֵי פְסוּלָהּ, מְטַמְּאָה בְגָדִים. לְאַחַר פְּסוּלָהּ, אֵינָהּ מְטַמְּאָה בְגָדִים. נִמְצְאָה חֻמְרָהּ, קֻלָּהּ. לְעוֹלָם מוֹעֲלִים בָּהּ, וּמַרְבִּין לָהּ עֵצִים, וּמַעֲשֶׂיהָ בַיּוֹם, וּבְכֹהֵן, הַמְּלָאכָה פוֹסֶלֶת בָּהּ, עַד שֶׁתֵּעָשֶׂה אֵפֶר, וְהַמְּלָאכָה פוֹסֶלֶת בַּמַּיִם, עַד שֶׁיַּטִּילוּ אֶת הָאֵפֶר: